Factoring numbers with a single interferogram

Abstract

We construct an analog computer based on light interference to encode the hyperbolic function f(ζ) = 1/ζ into a sequence of skewed curlicue functions. The resulting interferogram when scaled appropriately allows us to find the prime number decompositions of integers. We implement this idea exploiting polychromatic optical interference in a multipath interferometer and factor seven-digit numbers. We give an estimate for the largest number that can be factored by this scheme.

4 pages, 2 figures

References in corpus (7)

• Experimental demonstration of Shor's algorithm with quantum entanglement
• Demonstration of Shor's quantum factoring algorithm using photonic qubits
• Factorization of Numbers with the temporal Talbot effect: Optical implementation by a sequence of shaped ultrashort pulses
• Gauss sum factorization with cold atoms
• Factorizing Numbers with the Gauss Sum Technique: NMR Implementations
• NMR implementation of Factoring Large Numbers with GaußSums: Suppression of Ghost Factors
• NMR implementations of Gauss sums

Cited by in corpus (4)

• Multiboson Correlation Interferometry with arbitrary single-photon pure states
• Factorization of numbers with Gauss sums: I. Mathematical background
• Factorization of numbers with Gauss sums: II. Suggestions for implementations with chirped laser pulses
• Factorization of numbers with Gauss sums: III. Algorithms with Entanglement